So I have this equation:


And I know that

$${\left(a^b\right)}^c = a^{bc}$$

So I figured I'd simplify it into this:


And then further into this:


But for some reason, it doesn't appear to be working in all cases. What did I do wrong?

EDIT: In response to the Unclear what you're asking close votes, I am requesting assistance in finding the error in my simplification.

  • 1
    $\begingroup$ It's not true that $a^{b^c}=a^{b\cdot c}$, for instance, take $a=3,b=2,c=3$, we have $a^{b^c}=2^8=256$ but $a^{b\cdot c}=2^6=64$. $\endgroup$
    – user265675
    Dec 17, 2015 at 1:42
  • 3
    $\begingroup$ Your use of $x^{y^z}$ is ambiguous. It may mean $x^{\left(y^z\right)}$ or $\left(x^y\right)^z$. Most mathematicians use the former sense but you seem to be using it in the latter sense $\endgroup$
    – Henry
    Dec 17, 2015 at 1:44
  • $\begingroup$ @Mathos postimg.org/image/v1tefp7rr mathsisfun.com/algebra/exponent-laws.html $\endgroup$
    – warspyking
    Dec 17, 2015 at 1:45
  • $\begingroup$ @Henry that's probably my problem. I am evaluating it from left to right $\endgroup$
    – warspyking
    Dec 17, 2015 at 1:46
  • $\begingroup$ Also $\dfrac{y}{x} \times \dfrac{z}{x} \not = \dfrac{yz}{2x}$ unless $x=2$ or $yz=0$ $\endgroup$
    – Henry
    Dec 17, 2015 at 1:47

1 Answer 1


The problem most likely occurs in the way you are calculating your answers.

In general, a calculator will provide one answer to $a^{\frac1b}$, when there are actually $b$ existing roots.

Your math is perfectly fine, I believe it is your calculator that is the issue.

  • $\begingroup$ I'm running the EXACT same code in a Lua program. (Before the edits) as the arguments to print. $\endgroup$
    – warspyking
    Dec 17, 2015 at 2:00
  • $\begingroup$ Then it depends if the calculator does $x^a$ or $x^\frac1a$ first. Doing roots second produces more answers. Doing roots second produces less answers. Turning the whole fraction into decimals should give only one answer. $\endgroup$ Dec 17, 2015 at 2:04
  • $\begingroup$ Here's a screenshot: postimg.org/image/m68zlwgrt (equation, and then the evaluation of each step, then newline) $\endgroup$
    – warspyking
    Dec 17, 2015 at 2:05
  • $\begingroup$ If a screenshot of the code would help I have that as well: postimg.org/image/8ioscemfp $\endgroup$
    – warspyking
    Dec 17, 2015 at 2:14
  • $\begingroup$ I found the problem! Lua was evaluating a^b^c as a^(b^c). I added a set of brackets and good as new. Thanks! $\endgroup$
    – warspyking
    Dec 17, 2015 at 2:19

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